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Matematicheskie Zametki, 2024, Volume 115, Issue 2, Pages 276–285
DOI: https://doi.org/10.4213/mzm14116 (Mi mzm14116) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems

N. N. Nefedova

a Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm14116
Abstract: We study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems are obtained.
Keywords: singularly perturbed problem, periodic parabolic boundary value problem, reaction–diffusion equations, boundary and interior layers, asymptotic expansion, differential inequality, Lyapunov stability.
Funding agency Grant number
Russian Science Foundation 23-11-00069
This work was financially supported by the Russian Science Foundation, project no. 23-11-00069, https://rscf.ru/en/project/23-11-00069/.
Received: 25.07.2023
Revised: 27.10.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 2, Pages 232–239
DOI: https://doi.org/10.1134/S000143462401022X
Bibliographic databases:
Document Type: Article
UDC: 519.65
Language: Russian
Citation: N. N. Nefedov, “Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems”, Mat. Zametki, 115:2 (2024), 276–285; Math. Notes, 115:2 (2024), 232–239
Citation in format AMSBIB
\Bibitem{Nef24}
\by N.~N.~Nefedov
\paper Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction--Diffusion Systems
\jour Mat. Zametki
\yr 2024
\vol 115
\issue 2
\pages 276--285
\mathnet{http://mi.mathnet.ru/mzm14116}
\crossref{https://doi.org/10.4213/mzm14116}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4734359}
\transl
\jour Math. Notes
\yr 2024
\vol 115
\issue 2
\pages 232--239
\crossref{https://doi.org/10.1134/S000143462401022X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85190872378}
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    • This publication is cited in the following 1 articles:
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